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Hard · Stochastic Calculus · Quant Trader interview question · stochastic-calculus, merton-jump-diffusion, jump-process, probability
Merton's jump-diffusion model extends the geometric Brownian motion (GBM) model by incorporating jumps to account for sudden, unexpected price changes. The stochastic differential equation for Merton's jump-diffusion process is given by: $dS/S = \mu dt + \sigma dW + J dN$ where: $dS$ is the change in the asset price $S$ is the asset price $\mu$ is the drift rate $dt$ is the change in time $\sigma$ is the volatility $dW$ is a Wiener process (Brownian motion) $dN$ is a Pois